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Search: id:A013954
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| A013954 |
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sigma_6(n), the sum of the 6th powers of the divisors of n. |
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+0
82
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| 1, 65, 730, 4161, 15626, 47450, 117650, 266305, 532171, 1015690, 1771562, 3037530, 4826810, 7647250, 11406980, 17043521, 24137570, 34591115, 47045882, 65019786, 85884500, 115151530, 148035890
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.
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FORMULA
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G.f. sum(k>=1, k^6*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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MATHEMATICA
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lst={}; Do[AppendTo[lst, DivisorSigma[6, n]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
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PROGRAM
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(Other) sage: [sigma(n, 6)for n in xrange(1, 24)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
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CROSSREFS
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Sequence in context: A088677 A034680 A017675 this_sequence A116277 A008516 A000540
Adjacent sequences: A013951 A013952 A013953 this_sequence A013955 A013956 A013957
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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